Abstract
Interpolation subsets of a disk are described for some classes of analytic functions whose Fourier coefficients belong to the weighted class lp. For nontangent sets with a single condensation point the necessary and sufficient conditions for interpolation are obtained. For such spaces, it is proved that the natural description of the trace space is different. An explicit construction of the extension operator from functions defined on the interpolation set to the corresponding space of analytic functions is given. The obtained construction can be viewed as a generalization of Newton interpolation polynomials. Bibliography: 10 titles.
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